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| Preface List of Figures 0 Introduction 1 Analysis Without Lineaxization 2 Flow-Invariant Sets 3 Optimization 4 Control Theory 5 Notation 1 Proximal Calculus in Hilbert Space 1 Closest Points and Proximal Normals 2 Proximal Subgradients 3 The Density Theorem 4 Minimization Principles 5 Quadratic Inf-Convolutions 6 The Distance Function 7 Lipschitz Functions 8 The Sum Rule 9 The Chain Rule 10 Limiting Calculus 11 Problems on Chapter 1 2 Generalized Gradients in Banach Space 1 Definition and Basic Properties 2 Basic Calculus 3 Relation to Derivatives 4 Convex and Regular Functions 5 Tangents and Normals 6 Relationship to Proximal Analysis 7 The Bouligand Tangent Cone and Regular Sets 8 The Gradient Formula in Finite Dimensions 9 Problems on Chapter 2 3 Special Topics 1 Constrained Optimization and Value Functions 2 The Mean Value Inequality 3 Solving Equations 4 Derivate Calculus and Rademacher's Theorem 5 Sets in L2 and Integral b-~nctionals 6 Tangents and Interiors 7 Problems on Chapter 3 4 A Short Course in Control Theory 1 Trajectories of DiffercntiM Inclusions 2 Weak Invariance 3 Lipschitz Dependence and Strong Invariance 4 Equilibria 5 Lyapounov Theory and Stabilization 6 Monotonicity and Attainability 7 The Hamilton Jacobi Equation and Viscosity Solutions 8 Feedback Synthesis from Semisolutions 9 Necessary Conditions for Optimal Control 10 Normality and Controllability 11 Problems on Chapter 4 Notes and Comments List of Notation Bibliography Index |
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